Optimization of the Source Firing Pattern for X-Ray Scanning Systems

ABSTRACT

The present application discloses a computed tomography system having non-rotating X-ray sources that are programmed to optimize the source firing pattern. In one embodiment, the CT system is a fast cone-beam CT scanner which uses a fixed ring of multiple sources and fixed rings of detectors in an offset geometry. It should be appreciated that the source firing pattern is effectuated by a controller, which implements methods to determine a source firing pattern that are adapted to geometries where the X-ray sources and detector geometry are offset.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation application of U.S. patentapplication Ser. No. 14/688,898, entitled “Optimization of the SourceFiring Pattern for X-Ray Scanning Systems” and filed on Apr. 16, 2015,which is a continuation application of U.S. patent application Ser. No.13/405,117, of the same title, filed on Feb. 24, 2012, and issued asU.S. Pat. No. 9,046,465 on Jun. 2, 2015, which relies on U.S.Provisional Patent Application No. 61/446,098, entitled “Optimizationfor the Source Firing Pattern for Real Time Cone-Beam Tomography” andfiled on Feb. 24, 2011, for priority, all of which are hereinincorporated by reference in their entirety.

The present application is also related to U.S. patent application Ser.No. 13/146,645, filed on Jul. 27, 2011, which is a 371 national stageapplication of PCT/GB2010/050125, filed on Jan. 27, 2010 and which, inturn, relies in Great Britain Application No. 0901338.4, filed on Jan.28, 2009, for priority. Each of the aforementioned applications ishereby incorporated by reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 13/054,066, filed on Jan. 13, 2011, which is a 371 national stageapplication of PCT/GB2009/001760, filed on Jul. 15, 2009 and which, inturn, relies in Great Britain Application No. 0812864.7, filed on Jul.15, 2008, for priority. Each of the aforementioned applications ishereby incorporated by reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 13/063,467, filed on Mar. 11, 2011, which is a 371 national stageapplication of PCT/GB09/51178, filed on Sep. 13, 2009 and which, inturn, relies in Great Britain Application No. 0816823.9, filed on Sep.13, 2008, for priority. Each of the aforementioned applications ishereby incorporated by reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 13/032,593, filed on Feb. 22, 2011. Each of the aforementionedapplications is hereby incorporated by reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 12/787,930, filed on May 26, 2010, and which relies on U.S.Provisional Patent Application No. 61/181,068 filed on May 26, 2009, forpriority. Each of the aforementioned applications is hereby incorporatedby reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 12/788,083, filed on May 26, 2010, and which relies on U.S.Provisional Patent Application No. 61/181,070 filed on May 26, 2009, forpriority. Each of the aforementioned applications is hereby incorporatedby reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 13/086,708, filed on Apr. 14, 2011, which is a continuation of U.S.Pat. No. 7,949,101, filed on Jun. 16, 2009. Each of the aforementionedapplications is hereby incorporated by reference in its entirety.

The present application is related to U.S. patent application Ser. No.12/792,931, filed on Jun. 3, 2010, and which relies on U.S. ProvisionalPatent Application No. 61/183,591 filed on Jun. 3, 2009, for priority.Each of the aforementioned applications is hereby incorporated byreference in its entirety.

The present application is also related to U.S. patent application Ser.No. 13/346,705, filed on Jan. 9, 2012, which is a continuation of U.S.patent Ser. No. 12/835,682, filed on Jul. 13, 2010, and which relies onU.S. Provisional Patent Application No. 61/225,257 filed on Jul. 14,2009, for priority. Each of the aforementioned applications is herebyincorporated by reference in its entirety.

The present application is also related to U.S. patent application Ser.No. 12/787,878, filed on May 26, 2010, and which relies on U.S.Provisional Patent Application No. 61/181,077 filed on May 26, 2009, forpriority, which is:

-   -   1. A continuation-in-part of U.S. patent application Ser. No.        12/485,897, filed on Jun. 16, 2009, which is a continuation of        U.S. patent application Ser. No. 10/554,656, filed on Oct. 25,        2005, and now issued U.S. Pat. No. 7,564,939, which is a 371        national stage application of PCT/GB04/01729, filed on Apr. 23,        2004 and which, in turn, relies on Great Britain Application No.        0309387.9, filed on Apr. 25, 2003, for priority;    -   2. A continuation-in-part of U.S. Pat. No. 7,903,789, filed on        Feb. 16, 2009, which is a continuation of U.S. Pat. No.        7,512,215, filed on Oct. 25, 2005, which is a 371 national stage        application of PCT/GB2004/01741, filed on Apr. 23, 2004 and        which, in turn, relies on Great Britain Application Number        0309383.8, filed on Apr. 25, 2003, for priority;    -   3. A continuation-in-part of U.S. Pat. No. 7,664,230, filed on        Oct. 25, 2005, which is a 371 national stage application of        PCT/GB2004/001731, filed on Apr. 23, 2004 and which, in turn,        relies on Great Britain Patent Application Number 0309371.3,        filed on Apr. 25, 2003, for priority;    -   4. A continuation-in-part of U.S. patent application Ser. No.        12/033,035, filed on Feb. 19, 2008, and now issued U.S. Pat. No.        7,505,563, which is a continuation of U.S. patent application        Ser. No. 10/554,569, filed on Oct. 25, 2005, and now issued U.S.        Pat. No. 7,349,525, which is a 371 national stage filing of        PCT/GB04/001732, filed on Apr. 23, 2004 and which, in turn,        relies on Great Britain Patent Application Number 0309374.7,        filed on Apr. 25, 2003, for priority;    -   5. A continuation-in-part of U.S. Pat. No. 7,929,663, filed on        Apr. 12, 2010, which is a continuation of U.S. patent        application Ser. No. 12/211,219, filed on Sep. 16, 2008, and now        issued U.S. Pat. No. 7,724,868, which is a continuation of U.S.        patent Ser. No. 10/554,655, filed on Oct. 25, 2005, and now        issued U.S. Pat. No. 7,440,543, which is a 371 national stage        application of PCT/GB2004/001751, filed on Apr. 23, 2004, and        which, in turn, relies on Great Britain Patent Application        Number 0309385.3, filed on Apr. 25, 2003, for priority;    -   6. A continuation-in-part of U.S. Pat. No. 8,085,897, filed on        Jan. 29, 2010, which is a continuation of U.S. patent        application Ser. No. 10/554,570, filed on Oct. 25, 2005, and now        issued U.S. Pat. No. 7,684,538, which is a 371 national stage        application of PCT/GB2004/001747, filed on Apr. 23, 2004, and        which, in turn, relies on Great Britain Patent Application        Number 0309379.6, filed on Apr. 25, 2003, for priority;    -   7. A continuation-in-part of U.S. Pat. No. 7,876,879, issued on        Jan. 25, 2011 and U.S. patent application Ser. No. 12/142,005,        filed on Jun. 19, 2008, both of which are 371 national stage        applications of PCT/GB2006/004684, filed on Dec. 15, 2006,        which, in turn, relies on Great Britain Patent Application        Number 0525593.0, filed on Dec. 16, 2005, for priority;    -   8. A continuation-in-part of U.S. patent application Ser. No.        13/313,854, filed on Dec. 7, 2011, which is a continuation of        U.S. patent application Ser. No. 12/478,757, filed on Jun. 4,        2009, now issued U.S. Pat. No. 8,094,784, which is a        continuation of U.S. patent application Ser. No. 12/364,067,        filed on Feb. 2, 2009, which is a continuation of U.S. patent        application Ser. No. 12/033,035, filed on Feb. 19, 2008, and now        issued U.S. Pat. No. 7,505,563, which is a continuation of U.S.        patent application Ser. No. 10/554,569, filed on Oct. 25, 2005,        and now issued U.S. Pat. No. 7,349,525, which is a 371 national        stage filing of PCT/GB04/001732, filed on Apr. 23, 2004 and        which, in turn, relies on Great Britain Patent Application        Number 0309374.7, filed on Apr. 25, 2003, for priority. In        addition, U.S. patent application number relies on Great Britain        Patent Application Number 0812864.7, filed on Jul. 15, 2008, for        priority; and    -   9. A continuation-in part of U.S. patent application Ser. No.        12/712,476, filed on Feb. 25, 2010, which relies on U.S.        Provisional Patent Application No. 61/155,572 filed on Feb. 26,        2009 and Great Britain Patent Application No. 0903198.0 filed on        Feb. 25, 2009, for priority.        Each of the aforementioned PCT, foreign, and U.S. applications,        and any applications related thereto, is herein incorporated by        reference in their entirety.

FIELD

The present specification relates to X-ray scanning and, in particular,to the improved reconstruction of images generated by a computedtomography (CT) X-ray scanning system.

BACKGROUND

Three-dimensional images of the interior of objects are currentlygenerated, using conventional X-ray systems, for a variety of purposes,including security inspection, medical diagnostics, process imaging andnon-destructive testing. Several different system configurationscurrently exist for generating the image scanning data which is used tocreate the three-dimensional images.

In one exemplary system, X-ray source is rotated about the object underinspection. A collimated fan-beam of X-rays from the source passesthrough the object under inspection to a one-dimensional array of X-raydetectors located on the opposite side of the object from the source.Transmission X-ray data is collected at each of a number of angles toform a two-dimensional sinogram. This information is passed through animage reconstruction algorithm to create a two-dimensionalcross-sectional image of the object under inspection.

In another exemplary system, an X-ray source emits X-rays into a cone ofradiation which passes through the object to a two-dimensional array ofX-ray detectors which are directly opposed to the source. The source anddetector array are rotated about the object under inspection and theresulting X-ray projection data is reconstructed into athree-dimensional image.

In another exemplary system, the object being inspected is translatedalong a substantially linear trajectory, while the source and detectorassembly rotate in a plane perpendicular to the axis of object motion,to form an improved three-dimensional image. In this case, the sourcedescribes a helical motion about the object, the locus of source pointbeing situated on the surface of a cylinder about the object. The rateat which the object moves through the plane of the source and detectorsis related to the rate at which the source and detector assembly rotateabout the object, this ratio being described as the pitch of the helix.

Applicant has developed a new generation of X-ray systems that implementX-ray sources with more than one electron gun and one or more highvoltage anodes within a single vacuum envelope. In this system, an X-raysource allows non-sequential motion of an X-ray beam about an objectunder inspection through the use of multiple grid controlled electronguns which can be excited in any chosen sequence, the electron beam fromeach source being directed to irradiate anode sections which aredistributed around the object under inspection. This allows non-helicalsource trajectories to be described at high speeds consistent with therequirements for dynamic and high-throughput object imaging.Additionally, the rapid switching of electron guns under electrostaticcontrol enables the fast movement of the effective focal spot of theX-ray tube and the rapid generation of sets of tomographic X-ray scandata without the use of moving parts.

By configuring the firing sequence of the electron guns appropriately,an optimal set of X-ray projection data can be collected at rates farhigher than in conventional systems. Examples of such systems aredisclosed in the applications which are listed above and incorporatedherein by reference.

While Applicant has previously described an approach to sequentiallyfiring the electron guns, there is a need to develop an improved methodof optimally firing the sequence of electron guns to avoid the creationof image artifacts.

In particular, Applicant has recognized that the conventional helicalmotion of the X-ray source results in a sub-optimal sampling of theprojection space within the object with the consequent formation ofimage artifact due to this limited sampling. Applicant has furtherrecognized that, through the use of multi-emitter X-ray sourcetechnology, an optimal source firing sequence can be determined whichdoes not represent a helical scanning geometry and which would result inthe generation of improved three-dimensional images.

SUMMARY

In one embodiment, the present specification discloses an X-ray imagingapparatus for obtaining a radiation image of an object having a length,comprising: a plurality of X-ray tubes arranged in a first ring aroundthe object, each X-ray tube comprising a predefined number of X-raysources, each X-ray source being equally spaced from an adjacent source,each X-ray source emitting X-rays during a predefined emission period;and a controller configured to cause each of said X-ray sources to emitX-rays in accordance with a firing pattern, wherein said firing patterncauses a substantially even distribution of X-rays from the X-raysources over a surface of a virtual cylinder, having a length, whereinthe virtual cylinder is positioned around the object and the length ofthe virtual cylinder is equal to or greater than the length of theobject. The X-ray sources are stationary.

Optionally, the length of the virtual cylinder is equal to the length ofthe object plus a distance, wherein said distance is within a range of 0mm to 100 mm. The firing pattern causes the X-ray sources to emit X-raysin a non-sequential order. The firing pattern causes the X-ray sourcesto emit X-rays in a non-helical pattern. The firing pattern isrotationally invariant.

Optionally, the X-ray imaging apparatus defines a reconstruction volumecomprising a plurality of voxels, wherein X-rays intersect each voxel ofthe reconstruction volume at a plurality of angles and wherein saidplurality of angles are substantially evenly distributed over a range of0 degrees to 360 degrees. The X-ray imaging apparatus further comprisesa plurality of sensors arranged in a second ring around the object fordetecting X-rays emitted from the plurality of X-ray sources afterpassing through the object, wherein the sensors are offset from theX-ray sources along a predefined axis.

In another embodiment, the present specification discloses an X-rayimaging apparatus for obtaining a radiation image of an object having alength, comprising: a plurality of X-ray tubes, each X-ray tubecomprising a predefined number of X-ray sources and each X-ray sourceemitting X-rays during a predefined emission period, wherein the X-raysources are arranged in a circular pattern on a plane that is normal toa direction of travel of the object; and a controller configured tocause each of said X-ray sources to emit X-rays in accordance with afiring pattern, wherein said firing pattern causes said sources to firein a sequence that is rotationally invariant. During operation, theX-ray tubes are stationary.

Optionally, the object travels on a conveyor belt having a speed in arange of 250 mm/s to 500 mm/s. The firing pattern causes an evendistribution of X-rays from the X-ray sources over a surface of avirtual cylinder, having a length, wherein the virtual cylinder ispositioned around the object and the length of the virtual cylinder isequal to or greater than the length of the object. The length of thevirtual cylinder is equal to the length of the object plus a distance,wherein said distance is within a range of 0 mm to 100 mm.

Optionally, the X-ray imaging apparatus further comprises a plurality ofdetectors for generating projection data, wherein the controllermodifies the firing pattern based upon said projection data. Optionally,the X-ray imaging apparatus further comprises a plurality of detectorsfor generating projection data, wherein the sources and detectors, takenin combination, exhibit multi-fold symmetry.

In another embodiment, the present specification discloses an X-rayimaging apparatus defining a reconstruction volume, comprising aplurality of voxels, for scanning an object, comprising a plurality ofX-ray tubes, each X-ray tube comprising a predefined number of X-raysources and each X-ray source emitting X-rays during a predefinedemission period, wherein, during operation, the X-ray sources arestationary and wherein the X-ray sources are positioned in a plane; aplurality of detectors, wherein the detectors are on at least one planethat is parallel to the plane of the sources and for which the detectorsand the sources are not co-planar and wherein the detectors generateprojection data; and a controller configured to cause each of said X-raysources to emit X-rays in accordance with a firing pattern, wherein saidfiring pattern causes the X-ray sources to emit X-rays that intersecteach voxel of the reconstruction volume at a plurality of angles andwherein said plurality of angles are substantially evenly distributedover a range of 0 degrees to 360 degrees.

Optionally, the firing pattern causes an even distribution of X-raysfrom the X-ray sources over a surface of a virtual cylinder, having alength, wherein the virtual cylinder is positioned around the object andthe length of the virtual cylinder is equal to or greater than thelength of the object. The length of the virtual cylinder is equal to thelength of the object plus a distance, wherein said distance is within arange of 0 mm to 100 mm. The data storage requirements for animplementation of reconstruction methods using the projection data areless than data storage requirements for an implementation ofreconstruction methods using projection data generated from sequentialor helical firing patterns. The computational processing powerrequirements for an implementation of reconstruction methods using theprojection data are less than computational processing powerrequirements for an implementation of reconstruction methods usingprojection data generated from sequential or helical firing patterns.

The aforementioned and other embodiments of the present specificationshall be described in greater depth in the drawings and detaileddescription provided below.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features and advantages of the present specificationwill be further appreciated, as they become better understood byreference to the detailed description when considered in connection withthe accompanying drawings, wherein:

FIG. 1 shows an X-ray emitter suitable for use with the invention;

FIG. 2 is a diagram of an X-ray imaging system according to theinvention including a number of emitter units as shown in FIG. 1;

FIG. 3 is a diagram of the layout of an X-ray imaging system accordingto a second embodiment of the invention;

FIG. 4 is a diagram of the layout of an X-ray imaging system accordingto a third embodiment of the invention;

FIG. 5 illustrates an exemplary geometry of a real time tomography (RTT)system;

FIG. 6 illustrates the source positions on a regular lattice on thesurface of a cylinder;

FIG. 7(a) illustrates a first plot of a sampling pattern using a helicalgeometry;

FIG. 7(b) illustrates a second plot of a sampling pattern using a firingpattern produced by methods disclosed in the present application; and

FIG. 8 shows graphs of profiles of projection densities for differentfiring patterns.

DETAILED DESCRIPTION

The present specification is directed towards multiple embodiments. Thefollowing disclosure is provided in order to enable a person havingordinary skill in the art to practice the invention. Language used inthis specification should not be interpreted as a general disavowal ofany one specific embodiment or used to limit the claims beyond themeaning of the terms used therein. The general principles defined hereinmay be applied to other embodiments and applications without departingfrom the spirit and scope of the invention. Also, the terminology andphraseology used is for the purpose of describing exemplary embodimentsand should not be considered limiting. Thus, the present invention is tobe accorded the widest scope encompassing numerous alternatives,modifications and equivalents consistent with the principles andfeatures disclosed. For purpose of clarity, details relating totechnical material that is known in the technical fields related to theinvention have not been described in detail so as not to unnecessarilyobscure the present invention.

FIG. 1 shows a multi-emitter X-ray source 10 in which an anode 32 isirradiated by a set of electron guns 18, the whole assembly beinglocated within a vacuum envelope 25. Each electron source is controlledby an electrical potential which is applied to the electron gun assemblythrough a series of control pins 30. A common focus potential 28 cancontrol the focal spot of each electron gun the tube to balance spatialresolution in an image against thermal loading of the anode. One skilledin the art shall recognize that alternative electron gun arrangementsmay be configured to selectively irradiate regions of an anode and allsuch embodiments are covered within the scope of this application.

The multi-focus X-ray tube 10 comprises a ceramic former 12 and theelectron guns, or emitter elements, 18 extending along between the sides14, 16 of the former. A number of grid elements in the form of gridwires 20 are supported on the former 12 and extend over the gap betweenits two sides 14, 16 perpendicular to the emitter elements 18, but in aplane which is parallel to it. A number of focusing elements in the formof focusing wires 22 are supported in another plane on the opposite sideof the grid wires to the emitter elements. The focusing wires 22 areparallel to the grid wires 20 and spaced apart from each other with thesame spacing as the grid wires, each focusing wire 22 being aligned witha respective one of the grid wires 20.

The source 10 is enclosed in a housing 24 of an emitter unit 25 with theformer 12 being supported on the base 24 a of the housing. The focusingwires 22 are supported on two support rails 26 a, 26 b which extendparallel to the emitter elements 18, and are spaced from the former 12,the support rails being mounted on the base 24 a of the housing. Thesupport rails 26 a, 26 b are electrically conducting so that all of thefocusing wires 22 are electrically connected together. One of thesupport rails 26 a is connected to a connector 28 which projects throughthe base 24 a of the housing to provide an electrical connection for thefocusing wires 22. Each of the grid wires 20 extends down one side 16 ofthe former and is connected to a respective electrical connector 30which provide separate electrical connections for each of the grid wires20.

An anode 32 is supported between the side walls 24 b, 24 c of thehousing. The anode extends parallel to the emitter elements 18. The gridand focusing wires 20, 22 therefore extend between the emitter elements18 and the anode 32. An electrical connector 34 to the anode extendsthrough the side wall 24 b of the housing.

The emitter elements 18 are supported in the ends of the former and areheated by means of an electric current supplied to it via furtherconnectors 36, 38 in the housing.

In order to produce a beam of electrons from one position, a pair ofadjacent grid wires 20 can be connected to an extracting potential whichis positive with respect to the elements 18 while the remaining gridwires are connected to a blocking potential which is negative withrespect to the element 18. By selecting which pair of wires 20 is usedto extract electrons, the position of the beam of electrons can bechosen. As the X-rays will be emitted from the anode 32 at a point wherethe electrons strike it, the position of the X-ray source can also bechosen by choosing the extracting pair of grid wires. The focusingelements 22 are all kept at a positive potential with respect to thegrid wires 20 so that electrons extracted between any pair of the gridwires will also pass between, and be focused by, a corresponding pair offocusing elements 22.

FIG. 2 shows a suitable control system for a multi-emitter X-ray tubebased X-ray imaging system in which precise timing is maintained betweenthe grid control system (which determines the region of the anode to beirradiated) and acquisition of data from the X-ray sensor array. Animage reconstruction engine combines the two-dimensional projection datainto a three-dimensional data set for operator inspection.

An X-ray scanner 50 is set up in a conventional geometry and comprisesan array of emitter units 25 arranged in an arc around a central scanneraxis X, and orientated so as to emit X-rays towards the scanner axis X.A ring of sensors 52 is placed inside the emitters, directed inwardstowards the scanner axis. The sensors 52 and emitter units 25 are offsetfrom each other along the axis X so that X-rays emitted from the emitterunits pass by the sensors nearest to them, through the object, and aredetected by a number of sensors furthest from them. The number ofsensors 52 that will detect X-rays from each source depends on the widthof the fan of X-rays that is emitted from each source position in thetubes 25. The scanner is controlled by a control system which operates anumber of functions represented by functional blocks in FIG. 2.

A system control block 54 controls, and receives data from, an imagedisplay unit 56, an X-ray tube control block 58 and an imagereconstruction block 60. The X-ray tube control block 58 controls afocus control block 62 which controls the potentials of the focus wires22 in each of the emitter units 25, a grid control block 64 whichcontrols the potential of the individual grid wires 20 in each emitterunit 25, and a high voltage supply 68 which provides the power to theanode 32 of each of the emitter blocks and the power to the emitterelements 18. The image reconstruction block 60 controls and receivesdata from a sensor control block 70 which in turn controls and receivesdata from the sensors 52.

In operation, an object to be scanned is passed along the axis X, andX-ray beams are directed through the object from the X-ray tubes 25. Ineach scanning cycle each source position in each tube 25 is used once,the scanning cycle being repeated as the object moves along the axis X.Each source position produces a fan of X-rays which after passingthrough the object are detected by a number of the sensors 52.

In prior applications, Applicant described the order of X-ray emissionfrom the source positions in the tubes 25 as being chosen so as tominimize the thermal load on the X-ray tube. This was achieved byordering the emissions so that each source position is non-adjacent to,and therefore spaced from, the previous one and the subsequent one. Asdescribed below, the present specification discloses an improvedapproach to ordering X-ray emissions from the source positions in thetubes 25.

Various configurations of X-ray imaging system are covered within thescope of this application. For example, FIG. 3 shows a system in whichan object reconstruction space, defined by region 75, is irradiated by aseries of linear X-ray tube sections 60, 61, 62, 63, 64, each of whichcontain a series individual X-ray source emission points, i.e. 70, 71,72, 73, 74. The sources in each X-ray tube, labeled 1, 2, 3, 4, 5, canthen be fired in a predefined sequence.

FIG. 4 shows a system configuration where the image reconstructionregion 86 is surrounded by an array of source points 80 with a ring ofdetectors 82 being located in a plane adjacent to the plane of thesource points. The X-ray sources 80 are spaced around an axis X, withthe sensors 82 axially offset from the sources 80. When one of thesources 80 a emits an X-ray beam 84 this diverges, passes through theobject 86 and reaches a number of the sensors 82. When the sensors 82which are needed to detect X-rays from each of the source positions 80are known, source positions can be selected which can emitsimultaneously, provided that they do not require any common detectors.For example if there are 24 source positions 80 and 24 sensors 82 andeach source position requires 5 sensors, then four of the sensors 80 a,80 b, 80 c, 80 d, spaced around the object at 90° intervals can be usedsimultaneously.

In the present application, a computed tomography system havingnon-rotating X-ray sources is programmed to optimize the source firingpattern. In one embodiment, the CT system is a fast cone-beam CT scannerwhich uses a fixed ring of multiple sources and fixed rings of detectorsin an offset geometry. It should be appreciated that the source firingpattern is effectuated by a controller, having a processor and memoryfor storing a plurality of programmatic instructions. The instructionsare programmed to implement the source firing pattern methods disclosedherein. When the processor executes the instructions, the controllercauses the X-ray sources to fire in accordance with the determinedsource firing pattern.

It should further be appreciated that a computed tomography systemhaving non-rotating X-ray sources provides certain benefits, includingimproved scan time since time sinks caused by the physical rotation ofthe source around the object being scanned are eliminated. However,since the X-ray source and detector geometry are offset in thez-direction by some distance ε₁ 501, as shown in FIG. 5, imagereconstruction methodologies used in conventional rotating gantry CTsystems cannot be applied to this geometry. Methods to determine asource firing pattern, adapted to geometries where the X-ray sources anddetector geometry are offset, are therefore required.

Referring to FIG. 5, Z_(a) and C_(a) represent respectively the cylinderof radius ‘a’ with axis along the z-axis, and its boundary. The functionf, representing the object, is assumed to be supported on Z_(a,1) 502—asubset of Za of some finite length 1 and centered at the origin. Thesets of possible source and detector positions are given by C_(b) 503and C_(d) 504 respectively, where a<d<b. Let ε₂>ε₁>0 represent thesource-detector offsets in the z direction; then relative to some sourceposition xϵC_(b), the active detector region D_(x) 506 is the subset ofC_(d) defined by ε₁ 501, ε₂ 505 and the angular extents −γ, γ 507.

The geometry is assumed to be shift-invariant, so that the activedetector region is the same viewed from the perspective of any sourceposition xϵCb. Considering an arbitrary xϵCb, let Πα,x be a planecontaining x, and intersecting the transaxial plane containing x in aline tangent to Cb at x. This plane has equation y. α=s, for some sϵRand aϵS², the unit 2-sphere. Let L α,x be the line in Πα,x intersectingx and the z-axis. One may assume that the offsets ε₁, ε₂ are definedsuch that for any xϵCb, there exists αϵS² such that all rays in theplane Πα′, x, intersecting the support off and parallel to Lα′,x, for α′in some arbitrary small neighbourhood of α, are measured.

Accordingly, source point x lines in a plane which is separated from thelower edge of a two-dimensional array of detectors by a distance ε₁ andfrom the upper edge of the same detector array by a distance ε₂. Thesection of the detector array extends away from the plane intersectingthe axis of rotation and the center of the scan zone by a distance of ±Υ507. The source occupies points on the surface of a cylinder C_(b) 503while the detectors are on the surface of a cylinder C_(d) 504. Theobject is contained within a cylinder Z_(a,1) 502. The object movesalong axis z during a scan.

In one embodiment, system executes an optimal source firing sequencewhich provides uniform sampling of the projection space within theobject, thereby resulting in minimal image artifact. Here, the systemapplies a constraint to require uniform sampling of the projectionspace. This is summarised in the following equation:

ϕ=(k(i−1)mod N _(s))+1  (1)

where N_(s)=number of sources in the system, k=increment between firingsources, and i=projection number. Note that k=1 for a helical scan.

To find the optimal value of k, the objective is to fit the surface ofthe cylinder C_(b) 503 with a uniformly distributed triangulated mesh ofsource points 600, such as that shown in FIG. 6. Here, a suitable set ofequations for calculating k are

$\begin{matrix}{l_{1}^{2} = {d^{2} + \left( \frac{k^{- 1}p_{z}}{N_{s}} \right)^{2}}} & (2) \\{l_{2}^{2} = {\left( {2\; d} \right)^{2} + {p_{z}^{2}\left( {\frac{2\; k^{- 1}}{N_{s}} - 1} \right)}^{2}}} & (3) \\{l_{3}^{2} = {d^{2} + {p_{z}^{2}\left( {1 - \frac{k^{- 1}}{N_{s}}} \right)}^{2}}} & (4)\end{matrix}$

where d is the distance between adjacent sources, p_(z) is the z pitch,k⁻¹ is the inverse of k modulo N_(s) and l₁, l₂ and l₃ are the lengthsof the three side of each triangle.

In order to make the lattice triangles as equilateral as possible, thevalue of k⁻¹ is chosen to minimise the standard deviation of l₁, l₂ andl₃. The value of k is then chosen to make k⁻¹ as close as possible tothis value, since not all values of k have an inverse modulo N_(s).

More specifically, where the system has a set of discrete sourcesdenoted by S=s₁, . . . s_(S), a firing order of period 1 revolution canbe defined as the periodic extension of the sequence . . . , ϕ(1), . . ., ϕ(S); . . . , which is determined by some function ϕ: {1, . . . ,S}-→{1, . . . , S}.

This definition may be generalized to cover firing orders of anarbitrary period, R, revolutions. As stated above, the firing orderdetermines the sequence in which the physical sources in the RTT systemare switched on and off. For a particular firing order ϕ, as i runs from1 to S, the sources s_(ϕ(1)), . . . , s_(ϕ(S)) are switched in sequence.

While not required, it is preferable to construct a firing pattern thatmakes use of all sources, i.e. firing orders where the function ϕ isbijective (i.e. permutations of {1, . . . , S}. This ensures all sourcesare used and justifies the use of the term revolution, since a full setof projections from the physical sources s₁, . . . , s_(S) isconceptually analogous to, but substantially technically different from,a complete revolution of the gantry of a conventional CT scanner. Giventhis restriction, and the assumption that the firing order has period 1revolution, without loss of generality, one can adopt the conventionthat for any firing order, ϕ(1)=1.

For an RTT system with S sources, the firing order defined by thefunction ϕ is said to be order-1 rotationally invariant if for somefixed integer k we have:

ϕ(i)≡(ϕ(i+1)−k)(mod |S|),

i=1, . . . ,|S|  (5)

Interpreting this geometrically, this means that, from the perspectiveof some source s_(i), if the system moves to source s_(i+1), thepositions of all other sources in three-dimensional space, relative tothe source one is at, does not change. Stated differently, a system isrotationally invariant if it has multi-fold symmetry. In an exemplaryapplication, a system has a configuration of detectors and sensors thatexhibit 24 fold symmetry.

An order-1 rotationally invariant firing order is given by a function ϕof the form:

ϕ(i)=(k(i−1)mod |S|)+1;  (6)

where k is some integer co-prime to jSj, and is always of period 1revolution.

A special case of the order-1 rotationally invariant firing order is thesequential firing order. It is the period 1 firing order defined simplyby the identity mapping fi(i)=i, giving a classical single helicalsource trajectory.

Higher order rotationally invariant firing orders are necessarilydefined over periods of greater than one revolution, and can be viewedas a generalization of the order-1 case above, where the integer k ischosen such that gcd (k;N_(S))>1. If m=gcd (k;N_(S)) then the sequencecreated by (5) repeats every N_(S)/m sources. In order to avoid this, asecond increment q, is introduced that is coprime to k and that getsadded every N_(S)/m sources. If q=1, this can be expressed by functionsϕ_(r), for 1≤r≤N_(S)/m, defined as follows

ϕr(i)=[(k(i−1)+m(r−1)+[((i−1)m/NS)])mod NS)+1;  (7)

where [.] is the round towards negative infinity operator. Such a firingorder is often referred to as a multi-helix, since it can be viewed asdefining helical trajectories for multiple sources.

The choice of firing order is dictated to a certain extent by thereconstruction algorithm implemented. If an analytical algorithm is usedthat assumes some choice of source trajectory, then the firing patternshould approximate that trajectory. In order to consider the problem ofoptimizing the firing order in full generality, a method is requiredthat is independent of the choice of firing order.

In one embodiment, a firing order is selected that creates an evenlyspaced sampling lattice on the surface of a virtual cylinder. Thevirtual cylinder preferably defines a distance which exceeds the lengthof the object being scanned, plus sufficient length to allow the datacollection apparatus to cover all points in the object. In oneembodiment, the virtual cylinder has a length equal to the length of theobject plus an additional distance, such as 10, 50, or 100 mm or anyincrement therein. In a preferred embodiment, using a coordinate systemwhere zero is the center point of the virtual cylinder, the cylinder'slength is equal to the length of the object+/−50 mm. The firing patternis optimized such that even source coverage of the cylinder surface isachieved, namely that the distance between points on the cylindersurface are of equal length for as far as possible between adjacentsource points in all directions. Preferably, the even source coverageapplies to the full length of the virtual cylinder. With order-1rotationally invariant firing orders of the form (5), a firing order canbe constructed that gives close to an equilateral triangle samplinglattice on the surface of the cylinder.

Preferably, the firing order is chosen to get an even distribution ofthe angles of the X-rays intersecting each voxel of the reconstructionvolume over a range of 360 degrees and along the length of the object.Here, the angle is taken to mean the angle of the detector relative tothe source, in the projection of the X-ray onto a transaxial plane. Forexample, for a system with 768 sources, a firing order that satisfiesboth of these properties is given by substituting k=35 in (4).

A section of source point positions on the surface of the cylinder Cb isshown in FIGS. 7(a) and (b). FIG. 7(a) shows that the set of sourcepoints when k=1, i.e. a conventional helical scan firing pattern,describe lines across the surface, showing that large regions of thesurface are not covered. In contrast, FIG. 7(b) shows a triangularmapped array of source points which, for the system modeled, uses a kvalue source increment of 35.

To understand the practical impact of this non-helical sourcetrajectory, consider the data shown in FIG. 8, which depicts profiles ofprojection density along one line through the object (a line at thecenter of the projection volume perpendicular to the z-axis) with noobject in the beam. Graph 805 shows a profile through the projectionline density for a standard helical scan geometry, which demonstrates aconsiderable non-uniformity of projection density and leads toreconstructed image artifact, such as streaking. In contrast, graph 810shows a much more uniform projection density, obtained using the methodsdescribed herein, which produces a significantly cleaner reconstructedimage with little artifact due to error in sampling the projection data.

Additionally, an optimizing firing pattern, in accordance with themethods disclosed herein, enable an improved implementation ofreconstruction methods and, more particularly, minimizes data storagerequirements and/or computational processing power requirements for theimplementation of certain reconstruction algorithms, such as ART,methods that solves a set of linear equations, iterative linear equationsolvers, or any other reconstruction method that directly solves asystem of equations, on projection data generated by the firing patternsdisclosed herein relative to conventional firing patterns, such assequential or helical patterns.

The presently disclosed methodologies have a number of advantages.First, the accuracy of any image reconstruction algorithm dependscritically on the uniformity of projection density. By way of example,an algebraic reconstruction method is only as good as the equationswhich are available to it. A uniformly sampled projection space givesthe best possible set of equations for an algebraic reconstruction,thereby enabling the generation of high quality three dimensional imagesat high scan rates. For example, where the CT system having stationaryX-ray sources is configured as a bag or cargo scanner having a movingconveyor belt integrated therein, high quality three dimensional imagescan be generated even where the conveyor belt speed is faster than 200mm/s, such as 250 mm/s or 500 mm/s.

Second, the source firing order may be changed in direct response to themeasured projection data. For example, in the detection of a thin sheetof explosive material, X-ray attenuation along the length of the sheetis much greater than X-ray attenuation through the thickness of thesheet. Thus, the projection density in directions close to the long edgeof the sheet can be advantageously increased, if necessary at theexpense of projections through the plane of the sheet.

Third, a scanning system may be provided with multi-pass capability inwhich a first scan is conducted of the object with the evenlydistributed source firing pattern disclosed herein with further scansbeing conducted with revised source firing trajectories to mitigate forregions of exceptional X-ray attenuation in order to balance theprojection density of the scan overall. Accordingly, the source firingpattern for a given scan may be dynamically modulated based upon imagedata obtained from a prior scan.

Fourth, an X-ray scanning system may be constructed with a set ofsources and detectors that are chosen to exhibit multi-fold radialsymmetry. Here, uniform sampling can still be achieved, but the imagereconstruction process is simplified through the use of small sets ofcoefficients which are re-used multiple times, once for each symmetryorder.

Fifth, one can avoid having scanned regions with very high and very lowX-ray density, which typically occurs with a sequential firing order orhelical pattern. Where feed rates are sufficiently high, these regionscould actually create a nullspace. However, for a firing order optimizedas described herein, the distribution of X-ray density is much more evenand the distribution of the angles of the X-rays intersecting the regionis also more even. With the sequential firing order, there are regionswithin the reconstruction volume that are only illuminated from a verynarrow range of angles. With the optimized firing order describedherein, the distribution of the angles of the X-rays intersecting theregion is more even, thereby resulting in fewer limited angle typeartifacts in the data reconstructions.

In sum, for a CT scanner using switched sources and an offset detectorgeometry, the conventional helical source trajectory is far fromoptimal. Superior results are obtained using a firing order giving aneven lattice sampling of source points on the surface of a cylinder.

The above examples are merely illustrative of the many applications ofthe system of present invention. For example, while a system with 768sources has a k=35, it should be appreciated that systems with 384, 450or 900 sources would have different k values, i.e. a 384 source systemmay optimally have a k value of 25, depending upon the angulardistribution, or z pitch, of sampling. Although only a few embodimentsof the present invention have been described herein, it should beunderstood that the present invention might be embodied in many otherspecific forms without departing from the spirit or scope of theinvention. Therefore, the present examples and embodiments are to beconsidered as illustrative and not restrictive, and the invention may bemodified within the scope of the appended claims.

We claim:
 1. An X-ray imaging apparatus for obtaining a radiation imageof an object having a length, comprising: a. a plurality of X-ray tubesarranged in a first ring around the object, each X-ray tube comprising apredefined number of X-ray sources, each X-ray source being equallyspaced from an adjacent source, each X-ray source emitting X-rays duringa predefined emission period; and b. a controller configured to causeeach of said X-ray sources to emit X-rays in accordance with a firingpattern, wherein said firing pattern causes a substantially evendistribution of X-rays from the X-ray sources over a surface of avirtual cylinder, having a length, wherein the virtual cylinder ispositioned around the object and the length of the virtual cylinder isequal to or greater than the length of the object.
 2. The X-ray imagingapparatus of claim 1 wherein the length of the virtual cylinder is equalto the length of the object plus a distance, wherein said distance iswithin a range of 0 mm to 100 mm.
 3. The X-ray imaging apparatus ofclaim 1 wherein the X-ray sources are stationary.
 4. The X-ray imagingapparatus of claim 1 wherein the firing pattern causes the X-ray sourcesto emit X-rays in a non-sequential order.
 5. The X-ray imaging apparatusof claim 1 wherein the firing pattern causes the X-ray sources to emitX-rays in a non-helical pattern.
 6. The X-ray imaging apparatus of claim1 wherein the firing pattern is rotationally invariant.
 7. The X-rayimaging apparatus of claim 1 wherein the X-ray imaging apparatus definesa reconstruction volume comprising a plurality of voxels, wherein X-raysintersect each voxel of the reconstruction volume at a plurality ofangles and wherein said plurality of angles are substantially evenlydistributed over a range of 0 degrees to 360 degrees.
 8. An X-rayimaging apparatus of claim 1 further comprising a plurality of sensorsarranged in a second ring around the object for detecting X-rays emittedfrom the plurality of X-ray sources after passing through the object,wherein the sensors are offset from the X-ray sources along a predefinedaxis.
 9. An X-ray imaging apparatus for obtaining a radiation image ofan object having a length, comprising: a. a plurality of X-ray tubes,each X-ray tube comprising a predefined number of X-ray sources and eachX-ray source emitting X-rays during a predefined emission period,wherein the X-ray sources are arranged in a circular pattern on a planethat is normal to a direction of travel of the object; and b. acontroller configured to cause each of said X-ray sources to emit X-raysin accordance with a firing pattern, wherein said firing pattern causessaid sources to fire in a sequence that is rotationally invariant. 10.The X-ray imaging apparatus of claim 9 wherein, during operation, theX-ray tubes are stationary.
 11. The X-ray imaging apparatus of claim 10wherein the object travels on a conveyor belt having a speed in a rangeof 250 mm/s to 500 mm/s.
 12. The X-ray imaging apparatus of claim 9wherein the firing pattern causes an even distribution of X-rays fromthe X-ray sources over a surface of a virtual cylinder, having a length,wherein the virtual cylinder is positioned around the object and thelength of the virtual cylinder is equal to or greater than the length ofthe object.
 13. The X-ray imaging apparatus of claim 12 wherein thelength of the virtual cylinder is equal to the length of the object plusa distance, wherein said distance is within a range of 0 mm to 100 mm.14. The X-ray imaging apparatus of claim 9 further comprising aplurality of detectors for generating projection data, wherein thecontroller modifies the firing pattern based upon said projection data.15. The X-ray imaging apparatus of claim 9 further comprising aplurality of detectors for generating projection data, wherein thesources and detectors, taken in combination, exhibit multi-foldsymmetry.
 16. An X-ray imaging apparatus defining a reconstructionvolume, comprising a plurality of voxels, for scanning an object,comprising: a. a plurality of X-ray tubes, each X-ray tube comprising apredefined number of X-ray sources and each X-ray source emitting X-raysduring a predefined emission period, wherein, during operation, theX-ray sources are stationary and wherein the X-ray sources arepositioned in a plane; b. a plurality of detectors, wherein thedetectors are on at least one plane that is parallel to the plane of thesources and for which the detectors and the sources are not co-planarand wherein the detectors generate projection data; and c. a controllerconfigured to cause each of said X-ray sources to emit X-rays inaccordance with a firing pattern, wherein said firing pattern causes theX-ray sources to emit X-rays that intersect each voxel of thereconstruction volume at a plurality of angles and wherein saidplurality of angles are substantially evenly distributed over a range of0 degrees to 360 degrees.
 17. The X-ray imaging apparatus of claim 16wherein the firing pattern causes a substantially even distribution ofX-rays from the X-ray sources over a surface of a virtual cylinder,having a length, wherein the virtual cylinder is positioned around theobject and the length of the virtual cylinder is equal to or greaterthan the length of the object.
 18. The X-ray imaging apparatus of claim17 wherein the length of the virtual cylinder is equal to the length ofthe object plus a distance, wherein said distance is within a range of 0mm to 100 mm.
 19. The X-ray imaging apparatus of claim 16 wherein datastorage requirements for an implementation of reconstruction methodsusing the projection data are less than data storage requirements for animplementation of reconstruction methods using projection data generatedfrom sequential or helical firing patterns.
 20. The X-ray imagingapparatus of claim 16 wherein computational processing powerrequirements for an implementation of reconstruction methods using theprojection data are less than computational processing powerrequirements for an implementation of reconstruction methods usingprojection data generated from sequential or helical firing patterns.